Hi Juan,
There are 2 ways of doing it
1) You may follow similar upgrade process and select relevent technical usage to be upgraded
2) You may use SAINT to upgrade from 600 to 605.
Difference here is
In Option 1: Downtime will be less as compared to Option 2
While using Option 2 you may not be able to use the existing functionality until the upgrade is completed. It may result in abap dumps while doing so.
Hope this helps.
Regards,
Deepak Kori